Abstract
This chapter deals with the Rankine-Hugoniot relations connecting the states on both sides of a shock wave. These relationships are shown to produce important formulae connecting the pressure, density and temperature ratios on either side of the shock surface. In addition, other useful relationships are derived and presented in terms of the Mach number and the limiting form of these relationships in the case of weak and very strong shocks is discussed. The increase in the entropy of a gas on its passage through a shock is also considered. Finally, the reflection of a plane shock from a rigid plane surface is discussed and a relationship connecting the Mach numbers of the incident and reflected shocks is presented.
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References
M.A. Saad, Compressible Fluid Flow (Prentice-Hall, Inc., Englewood Cliffs, NJ, 1985), Chapter 4
J. Billingham, A.C. King, Wave Motion (Cambridge University Press, New York, 2000)
C.E. Needham, Blast Waves (Springer, Berlin, Heidelberg, 2010), Chapter 3
V. Babu, Fundamentals of Gas Dynamics, 2nd edn. (Wiley, Chichester, United Kingdom, 2015), Chapter 3
O. Regev, O.M. Umurhan, P.A. Yecko, Modern Fluid Dynamics for Physics and Astrophysics (Springer, New York, 2016), Section 6.5.2
J.H.S. Lee, The Gas Dynamics of Explosions (Cambridge University Press, New York, 2016), Chapter 1
R. Blum, Normal Shock Waves in a Compressible Fluid. Am. J. Phys. 35, 428 (1967)
L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Pergamon Press, London, 1966), Chapter 9
N. Curle, H.J. Davies, Modern Fluid Dynamics, vol 2 (Van Nostrand Reinhold Company, London, 1971), Chapter 3
R.C. Binder, Advanced Fluid Mechanics, vol 1 (Prentice-Hall, Upper Saddle River, NJ, 1958), Chapter 2
J.D. Anderson, Modern Compressible Flow with Historical Perspective, 3rd edn. (McGraw-Hill, New York, 2003), Chapter 7
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Prunty, S. (2019). Conditions Across the Shock: The Rankine-Hugoniot Equations. In: Introduction to Simple Shock Waves in Air . Shock Wave and High Pressure Phenomena. Springer, Cham. https://doi.org/10.1007/978-3-030-02565-6_3
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DOI: https://doi.org/10.1007/978-3-030-02565-6_3
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